Tooling: exact DAG union propagation speeds historical tensor audit 1.44x

research/disjoint-frame-unions/BENCHMARK.json

@@ -0,0 +1,143 @@
+{
+  "assignment_seed": 88,
+  "clock": "time.perf_counter",
+  "fresh_processes": true,
+  "implementation_sha256": {
+    "accelerator.py": "4b90cdf10e864d6a477c43ded3b3025c38cdf82f6c819b0a055795c31ddd9a02",
+    "benchmark.py": "1d16e3aaacb572fa8fab4185450e6c7d3280713b9c76d0937b173a26c2fb259a",
+    "verify.py": "b46d9c15f5583af2ef0b57f838a332ea841370483a503db730a588db94c1a02b"
+  },
+  "machine": "arm64",
+  "median_wall_seconds": {
+    "baseline": 5.014369041193277,
+    "propagated": 3.492928333580494
+  },
+  "note": "Local descriptive timings, not a speed threshold. Each complete audit includes source admission and byte-identical certificate comparison.",
+  "pairs": 5,
+  "platform": "macOS-27.0-arm64-arm-64bit-Mach-O",
+  "python": "3.14.4 (main, Apr  7 2026, 13:13:20) [Clang 21.0.0 (clang-2100.0.123.102)]",
+  "samples": [
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "baseline",
+      "pair": 0,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 5.00602824985981,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 5.052189417183399
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "propagated",
+      "pair": 0,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 3.446310624945909,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 3.4948033336549997
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "propagated",
+      "pair": 1,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 3.4012637501582503,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 3.4544588746502995
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "baseline",
+      "pair": 1,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 4.777637083083391,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 4.826718332711607
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "baseline",
+      "pair": 2,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 4.923342291731387,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 4.979373416397721
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "propagated",
+      "pair": 2,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 3.4429724160581827,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 3.492928333580494
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "propagated",
+      "pair": 3,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 3.608594875317067,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 3.6696084160357714
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "baseline",
+      "pair": 3,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 4.974850708153099,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 5.029562917072326
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "baseline",
+      "pair": 4,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 4.961562791839242,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 5.014369041193277
+    },
+    {
+      "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+      "engine": "propagated",
+      "pair": 4,
+      "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+      "scope": "complete_historical_audit",
+      "seconds": 3.373905540909618,
+      "source_files": 40,
+      "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+      "status": "PASS_DISJOINT_FRAME_UNIONS",
+      "wall_seconds": 3.427934500388801
+    }
+  ],
+  "speedup": 1.4355774188052695,
+  "status": "PASS_IDENTICAL_COMPLETE_CERTIFICATES"
+}

research/disjoint-frame-unions/CLAIM.md

@@ -0,0 +1,53 @@
+# Verification engineering, seed 88
+
+- OS assignment: `secrets.randbelow(100)` returned **88** on 2026-10-13.
+- Base: `2921874911956718fcaaaf9396fe8267b3cfa9f0` (freshly fetched main).
+- Claim: 2026-10-13 16:44 UTC. Expected finish: 17:20 UTC (13:20 Eastern),
+  reserving the final quarter for verification and handoff.
+- Object: the historical `DisjointTensor.frame_data` target-coordinate unions.
+- Method: propagate exact unions along the same reverse DAG traversal as the
+  unchanged reachable-target bitsets. Compare all three returned maps with
+  the original, run both frame orientations, and compare complete certificates.
+- Deliverable: additive opt-in adapter, differential/negative controls, pinned
+  sources, paired fresh-process timings, and one focused tooling PR; no new kappa.
+- No pinned issues existed; the two open issues were unrelated. Claim is local.
+
+Initial narrow candidates were Fano-completion reachability, subset-core ledger
+replay, and point-cancellation neighbor checks. Their complete certificates all
+finished below 0.25 seconds, so none justified optimization. One evidence-driven
+pivot selected the disjoint-tensor frame traversal: profiling the actual complete
+historical h=26 audit spent 2.34 of 8.53 instrumented seconds in `frame_data`.
+These exploratory instrumented timings are not the benchmark result.
+
+Seed 88 also fixes randomized topological-DAG cases, output permutations and
+mutation positions. The object and mechanism distinguish this contribution from
+existing optimizations; the seed is not itself a novelty claim.
+
+Overlap review read the 714-open-PR snapshot through #1019, the review ledger,
+selected #942 certificate/review/construction, local claims and relevant negative
+results. #950 considered and declined this traversal, choosing central-factor
+packing instead. #863 and #981 change historical root contraction/traversal
+choices; neither changes `frame_data`. #756 changes balanced-Fano enumeration,
+#778 changes single-intersection Gram construction, #976 changes historical
+rational rank, and #1006 changes T37 occupancy. None supplies this code.
+No closed mathematical search is reopened.
+
+Current selected conditional kappa at this base is 0.001661960547713947 from
+#942, with #890/#869/#870/#858 ancestry and unchanged #589 on #555. This tooling
+contribution concerns an older finite supplier and does not alter that frontier
+or its inherited all-size/compiler, realization, hosting, precision/tape,
+analytic or bit-interface assumptions.
+
+## Result
+
+Completed: the complete historical audit is 1.435577x faster in five alternating
+fresh-process pairs, with byte-identical complete receipts in all ten runs.
+All map entries/order, two physical orientations, independent BFS graph cases,
+and failure controls pass. `make verify-tests` passes 661 tests in 96 modules
+plus 20 patch checks. See README.md, BENCHMARK.json and VALIDATION.md.
+Final review found no competing frame-union implementation among 737 open PRs
+through #1042; #1029/#1041 are distinct U8 phase-recipe tools. No coordination
+issue was pinned. Source exploration ended before the final verification and
+handoff phase. The only additions are this optional package.
+
+Submitted contribution: [PR #1044](https://github.com/CrocSwap/integer-mult-bounds/pull/1044).

research/disjoint-frame-unions/NOTICE.md

@@ -0,0 +1,25 @@
+# Attribution and license
+
+This contribution is by Stephan Arrington (@steph4n-gh), with substantial
+OpenAI Codex assistance in implementation, experiment design, testing,
+mathematical explanation and packaging. A separately tasked Codex worker wrote
+the breadth-first graph oracle and reviewed the adapter. This is not independent
+human peer review. New material is under the repository's Apache-2.0 license.
+
+The unchanged disjoint-tensor construction, original frame-data verifier,
+phase checks, complete historical audit, and dirty-restoration tests are Douglas
+R. Colkitt's work, preserved at source commit
+`1a74950ce5074b848243ba89d8022fbadba66105`. Their precise base-source hashes are
+in SOURCES.json. The adapter retains the original descendant and source-union
+calculations and rectangle guard, replacing only target-union computation.
+
+The opt-in source-admission, complete-certificate comparison and alternating
+fresh-process benchmark follow Ross Richardson's incorporated PR950 package,
+`research/central-factor-packed/`, credited for that reproducibility pattern.
+No packed coefficient kernel is used here. Existing source notices and upstream
+Apache-2.0 material are unmodified.
+
+Concurrent PR863 by Curtis Dransfield and PR981 by @ToikY change root
+contraction/traversal recipes for this historical supplier. They are related
+construction research, not dependencies or this verifier optimization. Their
+source pins are not imported or represented as reviewed by this contribution.

research/disjoint-frame-unions/README.md

@@ -0,0 +1,131 @@
+# Exact target unions for the historical disjoint-tensor audit
+
+This opt-in adapter replaces repeated reachable-target enumeration with exact
+union propagation in `DisjointTensor.frame_data`. At h=26 it preserves all three
+maps on **60,372 active nodes**, including **9,206,600 reachable-target
+memberships**, and reproduces the **entire original historical certificate byte
+for byte**. The complete audit still checks integer coefficients, reversible
+embedding, both physical frame orientations, exact small residual bases,
+operation invoices, rational inequalities, guard slack and its original finite
+parameter screens.
+
+This is verification tooling: no new construction, kappa, search result, or
+multiplication runtime claim. The selected conditional result at the pinned base
+is PR942's **0.001661960547713947**. Historical bound strings in the reproduced
+certificate describe an earlier supplier.
+
+Five sequential alternating fresh-process pairs on macOS arm64 / Python 3.14.4
+measured median complete-audit wall time **5.014369 s → 3.492928 s (1.435577×)**.
+Every one of the ten runs reproduced the same full certificate. The measurement
+includes source admission, construction, scalar/frame checks, accounting and
+receipt comparison. BENCHMARK.json retains all samples, environment and code
+hashes. Timings describe this historical audit, not the selected frontier replay;
+there is no performance pass threshold. No other task-local tests or benchmarks
+were running during the measurement.
+
+## Reproduce
+
+Python 3.11+ and the standard library suffice. From the repository root:
+
+```sh
+python3 -I -B research/disjoint-frame-unions/verify.py
+```
+
+Expected status: `PASS_DISJOINT_FRAME_UNIONS`, with
+`scope: complete_historical_audit` and receipt SHA256
+`3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1`.
+This compares the complete original certificate, including every source hash,
+against the committed fixture; no fields are removed or normalized away.
+
+Additional reproducible checks:
+
+```sh
+python3 -I -B research/disjoint-frame-unions/test_unions.py
+python3 -I -O -B research/disjoint-frame-unions/test_unions.py
+python3 -I -B research/disjoint-frame-unions/test_replay.py
+python3 -I -B research/disjoint-frame-unions/verify.py --engine baseline
+python3 -I -B research/disjoint-frame-unions/benchmark.py --pairs 5 --output /tmp/disjoint-frame-unions.json
+```
+
+Use a new benchmark output path. Full inherited audit replay rejects `-O` to
+preserve inherited assertions. The new graph kernel and its independent tests
+also pass with assertions disabled; this is a distinct, narrower claim.
+
+## Equivalence argument
+
+For a node v let D(v) be its set of reachable output indices. If output i has
+ground-coordinate mask T_i, the old loop computes
+
+```
+U(v) = OR_{i in D(v)} T_i.
+```
+
+Define F(A) as the OR of T_i over indices in A. Then F(empty)=0 and
+F(A union B)=F(A) OR F(B). The original reverse topological pass initializes
+D at output nodes, then unions each child's D into each parent. The adapter
+initializes U at those same output nodes and propagates it alongside D.
+Induction in the identical reverse topological order gives U(v)=F(D(v)) at
+every node. Multiple outputs on one node and multiple paths to one output are
+handled by OR's idempotence. Target masks are actual output keys, not the
+positions of those keys in the sorted output list.
+
+The reachable-target bitsets are retained in full: later `bit_count` calls
+still see exactly the same D. Source unions and the nonempty/disjoint rectangle
+checks are unchanged. All three dictionaries preserve the original insertion
+order. The adapter assumes exactly the original graph contract: active nodes
+are closed under parents and topologically numbered. It is not a new DAG
+validator; the original full audit's acyclicity, support, coefficient and
+embedding checks remain in place.
+
+The old loop performs one target-mask lookup for every reachable-target
+membership (9,206,600 at h26). The replacement does one ground-mask OR per
+active parent edge. Python integers are unbounded; no hash, floating estimate,
+truncated bitmap or probabilistic acceptance is substituted for the exact sets.
+The full descendant bitset propagation and all later frame checks remain.
+
+This is a written equivalence argument plus finite independent controls, not a
+formal proof of the full multiplication theorem.
+
+## Coverage and failures
+
+`test_unions.py` contains eight tests, including five original historical tests
+run under a scoped adapter installation. It compares ordered contents of all
+three maps at h26, both full physical orientations, and exact small residual
+bases. A separately implemented breadth-first graph oracle checks 88 seeded
+arbitrary DAGs plus explicit small controls. Cases include aliased outputs,
+multiple-coordinate target masks, output insertion permutations, repeated
+children, an empty graph, and a 300-input graph with gaps in its active set.
+The BFS oracle is intentionally confined to small graphs; the h26 comparison
+uses the unmodified original implementation over every map entry.
+
+Four graph corruptions must retain the original explicit failure: source/target
+overlap, zero target union, an active node without an output path, and an alias
+that introduces overlap. The historical tests additionally cover corrupted
+coefficients/supports and all independent dirty inputs under both signed
+invocation directions.
+
+`test_replay.py` checks altered/missing source files, changed adapter bytes,
+changed or incomplete result fields, restoration after an audit exception,
+rejection of optimized full replay, and preservation of an existing output.
+The finite test domain and seed are fixed; no search or impossibility claim is
+made. The stopping rule is those tests plus five alternating benchmark pairs.
+
+## Pins and scope
+
+Exact base: `2921874911956718fcaaaf9396fe8267b3cfa9f0`.
+`SOURCES.json` binds 40 inherited files, including the original construction,
+all imported audit modules, fixture, tests, proof references and upstream files.
+Each inherited file hash was compared to its Git blob at that base. It also
+binds the new executable adapter, replay, tests and benchmark. Source admission
+precedes repository imports; unexpected imported repository scripts are rejected.
+
+The wrapper temporarily changes only `DisjointTensor.frame_data` and restores
+it even if the audit fails. No original source, certificate, source manifest,
+`upstream/` file or selected record is edited. This avoids invalidating existing
+consumers' immutable source pins, including the related PR950 package. Running
+the default repository commands does not automatically opt into this adapter.
+
+All inherited all-size/compiler, common-label/mutable-source, hosting,
+precision/tape, analytic and bit-interface assumptions remain. See NOTICE.md
+for predecessor attribution and AI disclosure, CLAIM.md for scope selection,
+and VALIDATION.md for the exact completed checks and remaining limitations.

research/disjoint-frame-unions/RELOCATION.json

@@ -0,0 +1,10 @@
+{
+  "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+  "engine": "propagated",
+  "receipt_sha256": "3f2b37542f9581f9d3238cccfce19fd3e2964c89ec4af4ff047fb8041f5c3cd1",
+  "scope": "complete_historical_audit",
+  "seconds": 3.3845524583011866,
+  "source_files": 40,
+  "source_manifest_sha256": "c413bf530a588b406b2f29e4ca0b82ca6f9612c0562a706609d0034c0d864ec4",
+  "status": "PASS_DISJOINT_FRAME_UNIONS"
+}